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Question

Show that limx0e1/x1e1/x+1 does not exist.

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Solution

Given

limx0e1x1e1x+1

Left hand limit.

L.H.L =limx0e101e10+1=e1e+1=010+1=1

we know that e=

e=1e=10
Right hand limit
R.H.L = limx0+1e0+1e10++1=e1e+1=e(11e)e(1+1e)
=101+0=1

So, here L.H.LR.H.L

So, limit does not exist.

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